Analyzes data from strip-split-plot experiments. Function strip_split_plot also analyzes strip-split-plot experiments replicated at several locations.

The type double function is imsls_d_strip_split_plot.

Address of a pointer to the memory location of a two dimensional, 22 by 6 array containing the ANOVA table. Each row in this array contains values for one of the effects in the ANOVA table. The first value in each row, anova_tablei,0 = anova_table[i×6], identifies the source for the effect associated with values in that row. The remaining values in a row contain the ANOVA table values using the following convention:

The Source Identifiers in the first column of anova_tablei,j are the only negative values in anova_table[]. Note that the p-value for the F-statistic is returned as 0.0 when the value is so small that all significant digits have been lost. Assignments of identifiers to ANOVA sources use the following coding:

Notes: † If n_locations=1 sources involving location are set to missing (NaN).

Function imsls_f_strip_split_plot is capable of analyzing a wide variety of strip-split plot experiments, also referred to as strip-strip plot experiments. By default, imsls_f_strip_split_plot assumes that both strip-plot factors, and split-plots are fixed effects, and the location effects, if any, are random effects. The nature of randomization used in an experiment determines analysis of the data. Two popular forms of randomization in strip-plot and split-plot experiments are illustrated in the following two figures. In both experiments, the strip-plot factor, factor A, has 4 levels that are randomly assigned to a block or field in four strips.

In the strip-plot experiment, factor B, has 3 levels that are randomly assigned as strips across each of the four levels of factor A. In this case, factors A and B are completely crossed. The randomization applied to factor B is independent of the application of the strip-plots, factor A.

Contrast this to the randomization depicted in Table 4.30. In this split-plot experiment, the levels of factor B are nested within each level of factor A whole-plots. Factor B is randomized independently within each level of factor A. Unlike the strip-plot experiment, in the split-plot experiment different levels of factor B appear in the same row.

A strip-split plot experiment is a strip-plot experiment with a third factor randomized within each level of strip-plot factor A, see Table 4.31. The third factor, referred to as the split-plot factor, is randomly assigned to experimental units within each level of strip-plot factor A. imsls_f_strip_split_plot analyzes strip-split plot experiments consisting of two strip-plot factors and one split-plot factor nested within strip-plot factors A and B.

Strip-split plot experiments are closely related to split-split plot experiments, see Table 4.32. The main difference between the two is that in strip-split plot experiments, the order of the levels for factor B are not applied randomly across factor A. Each level of factor B is constant across any row. In this example, the entire first row is assigned to the third level of factor B. In the equivalent split-split plot experiment, the levels of factor B are not constant across any row. The levels are randomized within each level of factor A.

In some studies, a strip-split-plot experiment is replicated at several locations. Function imsls_f_strip_split_plot can analyze strip-split plot experiments replicated at multiple locations, even when the number of blocks or replicates at each location might be different. If only a single replicate or block is used at each location, then location should be treated as a blocking factor, with n_locations=1. If n_locations=1, it is assumed that either the experiment was conducted at multiple locations, each with a single block, or at a single location with more than one block or replicate at that location. When n_locations=1, all entries associated with location in the anova table will contain missing values.

However, if n_locations>1, it is assumed the experiment was repeated at multiple locations, with blocking occurring at each location. Although the number of blocks at each location can be different, the number of levels for the strip-plot and split-plot factors strip-plots must be the same at each location. The locations associated with each of the observations in y are specified in the argument locations[], which is a required input argument when n_locations>1.

By default, locations are assumed to be random effects. Tests involving strip-plots use the interaction between strip-plots and locations as the error term for testing whether there are statistically significant differences among strip-plots. However, this assumes that the interaction of strip-plots and locations is not statistically significant. A test of this assumption is included in the anova table. If any interactions between locations and strip-plot or split-plot factors are statistically significant, then the nature of these interactions should be explored since this impacts the interpretation of the significance of the treatment factors.

Similarly, when locations are assumed to be random effects, tests involving split-plots do not use the split-plot errors pooled across locations. Instead, the error term for split-plots is the interaction between locations and split-plots.

Suppose, for example, that a researcher wanted to conduct an agricultural experiment comparing the effectiveness of 4 fertilizers with 3 seed lots and 3 rates of application. One replicate of the experiment is conducted at each of the 3 farms. That is, only a single field at each location is assigned to this experiment.

Each field is divided into 4 vertical strips and 3 horizontal strips. The vertical strips are randomly assigned to fertilizers and the rows are randomly assigned to application rates. Fertilizers and application rates represent strip-plot factors A and B respectively. Seed lots are randomly assigned to three sub-divisions within each combination of strip-plots.

In this case, each farm is a blocking factor, fertilizers are factor A strip-plots, fertilizer application rates are factor B strip-plots, and seed lots are split-plots. The input array rep would contain integers from 1 to the number of farms.

The experiment was conducted using a 2 x 2 strip_split plot arrangement with each of the four plots divided into 2 sub-divisions that were randomly assigned one of two split-plot levels. This was replicated 3 times producing an experiment with n = 2x2x2x3 = 24 observations.